Mirror symmetry breaking of superradiance in a dipolar BEC Bojeong Seo1Mingchen Huang1Ziting Chen1Mithilesh K. Parit1Yifei He1Peng Chen1and Gyu-Boong Jo1 2

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Mirror symmetry breaking of superradiance in a dipolar BEC

Bojeong Seo,1, ∗Mingchen Huang,1, ∗Ziting Chen,1Mithilesh

K. Parit,1Yifei He,1Peng Chen,1and Gyu-Boong Jo1, 2, †

1Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

2IAS Center for Quantum Technologies, The Hong Kong University of Science and Technology, Kowloon, Hong Kong, China

Dicke superradiance occurs when two or more emitters cooperatively interact via the electro-

magnetic ﬁeld. This collective light scattering process has been extensively studied across various

platforms, from atoms to quantum dots and organic molecules. Despite extensive research, the

precise role of direct interactions between emitters in superradiance remains elusive, particularly in

many-body systems where the complexity of interactions poses signiﬁcant challenges. In this study,

we investigate the eﬀect of dipole-dipole interaction between 18,000 atoms in dipolar Bose-Einstein

condensates (BECs) on the superradiance process. In dipolar BECs, we simplify the complex eﬀect

of anisotropic magnetic dipole-dipole interaction with Bogoliubov transformation. We observe that

anisotropic Bogoliubov excitation breaks the mirror symmetry in decay modes of superradiance.

Collective light scattering [1], a cooperative emission

process inducing directional scattered atoms, has been

observed in various atomic systems ranging from ther-

mal atoms [2, 3], degenerate Bose gases [4–12], free

fermions [13] to atoms coupled to the cavity mode [14–

16]. Among them, a Bose-Einstein condensate (BEC) has

served as a promising platform for exploring a superra-

diant light scattering process owing to its unique coher-

ence property with [4–12, 17] and without external light

ﬁelds [18–21]. When the external light shines on atoms

in the condensate, collective scattering of light creates a

quasiparticle in the form of recoiling atoms that interfere

with condensate atoms at rest, leading to the generation

of matter-wave grating that is further enhanced by sub-

sequent light scattering [22]. So far, however, prior stud-

ies have primarily focused on a non-interacting regime,

leaving the eﬀect of interactions largely unexplored [23–

26]. This makes it challenging to explore exotic states

of matter using light scattering even though fundamen-

tal excitations in exotic states are expected to manifest

themselves in the light-matter interaction process [27].

In this work, we investigate a superradiance light scat-

tering process from a dipolar BEC in an elongated trap,

in which the mirror symmetry in superradiance is bro-

ken due to the dipolar intearction. Here, magnetic dipo-

lar interactions result in anisotropic dispersion of dipo-

lar superﬂuid [24, 25], which allows us to control the

asymmetry of superradiant peaks by changing the direc-

tion of the external magnetic ﬁeld. Such dipolar eﬀects

in quantum gases [28] have recently opened up a new

regime where anisotropic dipole-dipole interactions play

a crucial role in realizing new phases of matter, such as

quantum droplets and supersolids [28]. Our work demon-

strates how fundamental excitations begin to contribute

and manifest themselves in light-matter interaction pro-

cesses.

∗These authors contributed equally.

†gbjo@ust.hk

Experiment We initiate experiments with a quasi-

one-dimensional dipolar BEC of approximately 1.8×104

erbium (168Er) atoms in the |MJ=−6⟩state [29–31]. By

aligning the dipole orientation along a speciﬁed direction

(parallel to an external magnetic ﬁeld), we excited the

ground state BEC at |q= 0⟩to an excited state |e⟩using

a largely detuned pump beam. This excited state then

decays back to the ground state, acquiring non-zero mo-

mentum in the process due to momentum conservation.

In a typical condensate without dipolar interactions, this

scattering process is ampliﬁed along the long axis of the

condensate [4–6]. It leads to decay in two opposite direc-

tions symmetrically and emits photons with momentum

ℏk583, where k583 represents the wavevector of the pump

beam. As a result of this symmetric light-scattering pro-

cess, the quasi-particles are created with the momentum

of √2ℏk583 along the 45◦relative to the long-axis of the

condensate ((see Fig. 1(a)). We can simplify our model

by eliminating the intermediate excited state and con-

sidering a two-level system comprising the initial state

at |q= 0⟩and a ﬁnal state at |q=√2ℏk583⟩, owing to

the relatively large detuning (∆) of the pump beam com-

pared to the Rabi frequency (Ω) of the driving ﬁeld and

the spontaneous emission rate from |e⟩to |q=k583⟩.

A distinct feature of a dipolar BEC, as opposed

to one with only isotropic contact interactions, is its

anisotropic dispersion relation due to dipole-dipole inter-

actions. The elementary anisotropic dipolar Bogoliubov

excitation spectrum, ℏω(q), for a uniform density nis

expressed as

ℏω(q) = pE(q)(E(q)+2gn(1 + ϵdd(3 cos2ϕ−1))) (1)

where E(q) = ℏ2q2

2mand ϕis the angle between the ex-

ternal magnetic ﬁeld and the atomic excitation direc-

tion. Here, g= 4πℏ2as/m with atomic mass mand

ϵdd =add/asfor the characterisitc dipolar length of

add=66.3a0. This leads to a broken symmetry in the two

end-ﬁre modes, as evident from the asymmetry in their

decay rates, Γ′

L̸= Γ′

R(see Fig. 1(b)). In consequence,

one decay channel becomes dominant in the scattering

arXiv:2210.01586v4 [cond-mat.quant-gas] 13 Sep 2024

Pump Beam

B-field

Recoiled atoms

Dipolar BEC

Udd ~ (1-3 cos2 α)

Optical density

Scattered light

Adiabatic elimination

FIG. 1. Mirror symmetry breaking of the superradi-

ance in a dipolar BEC (a) A quasi-1D dipolar conden-

sate is exposed to the pump beam propagating along the +y

axis. Due to the anisotropic dipolar interaction presented in

the dipolar BEC (circular inset), the Bogoliubov excitation

spectrum becomes anisotropic, leading to the mirror symme-

try breaking for two exciations along the elongated direction

of the condensate. As a result, we observe the asymmetric

outcoupled atoms after the expansion of the cloud. (b) The

superradiance process can be simpliﬁed by adiabatically elim-

inating the intermediate state |e⟩for a suﬃciently large detun-

ing δ= 6.6MHz, compared to the optical linewidth. Given

the anisotropic dispersion spectrum, the two ﬁnal ground

states, |qR⟩or |qL⟩, are shifted in energy with diﬀerent tran-

sition rates. (c) Time-of-ﬂight image of asymmetric superra-

diant dipolar BEC.

process, leading to an observed increase in atoms in one

of the two collective excitation (see Fig. 1(c)).

To conﬁrm that the observed asymmetric scattering is

a collective phenomenon and not typical spontaneous Ra-

man scattering, we measure the dynamic change in the

scattering rate of atom decay. In Fig.2(a), we observe

the burst in scattering, which is consistent with quantum

Monte-Carlo simulations, conﬁrming the distinct collec-

tive nature of this interaction. To simulate this behavior,

we solve the Lindblad master equation,

ρ(t) = −i

ℏ[H, ρ(t)] + X

Γi

2L(ρ),(2)

that describes the superradiant decay rate of Natoms

with multiple decay modes, Γi. The decay rate can be

estimated by taking the time derivative of the population

of the ground state. Assuming two decay modes, ΓLand

ΓR, the Lindblad equation can be simpliﬁed to ρ(t) =

Γ’t

Rscat (arb. unit)

₀

(normalized)

Γ’t

N = 40

N = 90

N = 160

N = 500

N = 20000 (exp.)

1.0

0.2

0.4

0.6

0.8

10 -1

10 -2

10 -3

0˚

30˚

45˚

75˚

90˚

180˚

Peak time

10 -1

10 -2

10 104

10-3 10-2 10-1 100

0.0

0.2

0.4

0.6

0.8

1.0

Angle (θ)

0.0022 0.0028

0.0

0.6

FIG. 2. Collective enhancement of the atom-light scat-

tering in dipolar BEC (a) Bursts in the dicke superradiance

with the measurement and the simulation. Data is normalized

such that the peak Rscat are set to 1. Inset shows the time

of peak scattering for diﬀerent number of atoms. (b) Change

of the ground state population (N0) against the change of

Γ′t. The dashed line shows the calculated single atom Ra-

man scattering. N0is normalized such that maximum N0is

ΓL

2L(ρ)+ ΓR

2L(ρ). We use a quantum Monte Carlo solver

in the Quantum Toolbox in Python (QuTiP) [32] to solve

this equation.

As more atoms participate in the collective emission

process, the peak scattering time advances, as shown in

Fig.2.a and its inset. In Fig.2(b), we also conﬁrm en-

hanced decay to the ground state in asymmetric cases

(θ=π/6, π/4, and 5π/12), indicating superradiance even

when mirror-symmetry is broken. The ground state pop-

ulation resulted from the typical spontaneous Raman

scattering without collective scattering is provided as a

comparison (dashed line).

Mirror-symmetry breaking in superradiance

Next we examine the mirror-symmetry breaking mech-

anism with the statistical analysis of our measurements.

In Fig. 3, we characterize a superradiant sample by

recording an asymmetry of superradiant peaks. For each

condition, we obtain around 170-300 data and plotted

a histogram for an asymmetry ratio (Rasym =NR−NL

NR+NL)

where NR(NL) represents the atom number of right (left)

superradiant peak. When the left (right) atom cloud is

dominant, the mean value of the histogram has a negative

(positive) value.

Scattering events create two quasi-particle excitations,

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MirrorsymmetrybreakingofsuperradianceinadipolarBECBojeongSeo,1,∗MingchenHuang,1,∗ZitingChen,1MithileshK.Parit,1YifeiHe,1PengChen,1andGyu-BoongJo1,2,†1DepartmentofPhysics,TheHongKongUniversityofScienceandTechnology,ClearWaterBay,Kowloon,HongKong,China2IASCenterforQuantumTechnologies,TheHongKongUniver...

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Mirror symmetry breaking of superradiance in a dipolar BEC Bojeong Seo1Mingchen Huang1Ziting Chen1Mithilesh K. Parit1Yifei He1Peng Chen1and Gyu-Boong Jo1 2

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